学习笔记 第四周 第二篇

Posted 2020-06-26 jinkehust

仿真作业

 

对于老师所给的交流电机模型，其正常工作时，旋转磁场的转速

n₀=60f/p=1500r/min

一般情况下，三相异步电动机的额定转速n_N=(0.94~0.985) n₀，运行老师所给的电机模型，知该电机的额定转速约为1490r/min

 

1. 启动方法的选择

　　总体要求是，在保证电流较小的情况下，拥有较大的启动转矩。

　　参考书P70几种常用启动方法的比较可知，在启动电流相同的情况下，自耦变压器降压启动的启动转矩较大。Y-△降压启动也有良好的启动特性，但考虑到自耦变压器降压启动的K值可变，选择性更多，利于后面进行调节，因此选用自耦变压器降压启动的启动。

 

　　选取K=0.8

 

     2. 调速方法的选择

　　要求满足相应速比进行调速。

　　选用变频调速，因为其调速范围广，且能保证电机的机械特性硬度不变，在n=0时有较大的启动转矩，利于启动。

　　具体频率比的值要通过调试得出。

 

     3. 制动方法的选择

　　依题意，采取倒拉制动的制动效果会好于能耗制动，选用倒拉制动，但与此同时，倒拉制动并不能自动在n=0时停止，因此需要及时进行控制。

 

 

　　启动阶段为t=100-110ms，t=310ms时转速稳定在800r/min

　　匀速运动0.5s，从t=310ms至t=810ms

　　从810ms开始倒拉制动至转速为0。从t=1000ms至t=1500ms保持静止。

　　从t=1500ms开始反向加速，t=1750ms时转速稳定在600r/min

　　匀速运动0.6s,从t=1650ms至t=2250ms

　　从2250ms开始制动，至2570ms制动至静止。

　　整个过程耗时2570ms，期间转矩Tm始终控制在200以下。

 

 

　　代码如下：

model SACIM "A Simple AC Induction Motor Model"

type Voltage=Real(unit="V");

type Current=Real(unit="A");

type Resistance=Real(unit="Ohm");

type Inductance=Real(unit="H");

type Speed=Real(unit="r/min");

type Torque=Real(unit="N.m");

type Inertia=Real(unit="kg.m^2");

type Frequency=Real(unit="Hz");

type Flux=Real(unit="Wb");

type Angle=Real(unit="rad");

type AngularVelocity=Real(unit="rad/s");

 

constant Real Pi = 3.1415926;

 

Current i_A"A Phase Current of Stator";

Current i_B"B Phase Current of Stator";

Current i_C"C Phase Current of Stator";

Voltage u_A"A Phase Voltage of Stator";

Voltage u_B"B Phase Voltage of Stator";

Voltage u_C"C Phase Voltage of Stator";

Current i_a"A Phase Current of Rotor";

Current i_b"B Phase Current of Rotor";

Current i_c"C Phase Current of Rotor";

Frequency f_s"Frequency of Stator";

Torque Tm"Torque of the Motor";

Speed n"Speed of the Motor";

 

Flux Psi_A"A Phase Flux-Linkage of Stator";

Flux Psi_B"B Phase Flux-Linkage of Stator";

Flux Psi_C"C Phase Flux-Linkage of Stator";

Flux Psi_a"a Phase Flux-Linkage of Rotor";

Flux Psi_b"b Phase Flux-Linkage of Rotor";

Flux Psi_c"c Phase Flux-Linkage of Rotor";

 

Angle phi"Electrical Angle of Rotor";

Angle phi_m"Mechnical Angle of Rotor";

AngularVelocity w"Angular Velocity of Rotor";

 

Torque Tl"Load Torque";

 

Resistance Rs"Stator Resistance";

parameter Resistance Rr=0.408"Rotor Resistance";

parameter Inductance Ls = 0.00252"Stator Leakage Inductance";

parameter Inductance Lr = 0.00252"Rotor Leakage Inductance";

parameter Inductance Lm = 0.00847"Mutual Inductance";

parameter Frequency f_N = 50"Rated Frequency of Stator";

parameter Voltage u_N = 220"Rated Phase Voltage of Stator";

parameter Real p =2"number of pole pairs";

parameter Inertia Jm = 0.1"Motor Inertia";

parameter Inertia Jl = 0.1"Load Inertia";

parameter Real K=0.8"starting rate";

parameter Real a=0.54"frequency rate";

parameter Real b=0.0546"stable frequency rate";

parameter Real c=0.3948"another frequency rate";

parameter Real P=0.7"stoping rate";

 

initial equation

 

Psi_A = 0;

Psi_B = 0;

Psi_C = 0;

Psi_a = 0;

Psi_b = 0;

Psi_c = 0;

phi = 0;

w = 0;

 

equation

 

u_A = Rs * i_A + 1000 * der(Psi_A);

u_B = Rs * i_B + 1000 * der(Psi_B);

u_C = Rs * i_C + 1000 * der(Psi_C);

 

0 = Rr * i_a + 1000 * der(Psi_a);

0 = Rr * i_b + 1000 * der(Psi_b);

0 = Rr * i_c + 1000 * der(Psi_c);

 

Psi_A = (Lm+Ls)*i_A + (-0.5*Lm)*i_B + (-0.5*Lm)*i_C + (Lm*cos(phi))*i_a + (Lm*cos(phi+2*Pi/3))*i_b + (Lm*cos(phi-2*Pi/3))*i_c;

Psi_B = (-0.5*Lm)*i_A + (Lm+Ls)*i_B + (-0.5*Lm)*i_C + (Lm*cos(phi-2*Pi/3))*i_a + (Lm*cos(phi))*i_b + (Lm*cos(phi+2*Pi/3))*i_c;

Psi_C = (-0.5*Lm)*i_A + (-0.5*Lm)*i_B + (Lm+Ls)*i_C + (Lm*cos(phi+2*Pi/3))*i_a + (Lm*cos(phi-2*Pi/3))*i_b + (Lm*cos(phi))*i_c;

 

Psi_a = (Lm*cos(phi))*i_A + (Lm*cos(phi-2*Pi/3))*i_B + (Lm*cos(phi+2*Pi/3))*i_C + (Lm+Lr)*i_a + (-0.5*Lm)*i_b + (-0.5*Lm)*i_c;

Psi_b = (Lm*cos(phi+2*Pi/3))*i_A + (Lm*cos(phi))*i_B + (Lm*cos(phi-2*Pi/3))*i_C + (-0.5*Lm)*i_a + (Lm+Lr)*i_b + (-0.5*Lm)*i_c;

Psi_c = (Lm*cos(phi-2*Pi/3))*i_A + (Lm*cos(phi+2*Pi/3))*i_B + (Lm*cos(phi))*i_C + (-0.5*Lm)*i_a + (-0.5*Lm)*i_b + (Lm+Lr)*i_c;

 

Tm =-p*Lm*((i_A*i_a+i_B*i_b+i_C*i_c)*sin(phi)+(i_A*i_b+i_B*i_c+i_C*i_a)*sin(phi+2*Pi/3)+(i_A*i_c+i_B*i_a+i_C*i_b)*sin(phi-2*Pi/3));

 

w = 1000 * der(phi_m);

 

phi_m = phi/p;

n= w*60/(2*Pi);

 

Tm-Tl = (Jm+Jl) * 1000 * der(w);

Tl = 10;

 

if time <= 100 then

f_s = 0;

Rs = 0.531;

u_A = 0;

u_B = 0;

u_C = 0;

 

elseif time<=110 then

f_s = f_N*a;

Rs = 0.531;

u_A = u_N * 1.414 * sin(2*Pi*f_s*time/1000)*K*a;

u_B = u_N * 1.414 * sin(2*Pi*f_s*time/1000-2*Pi/3)*K*a;

u_C = u_N * 1.414 * sin(2*Pi*f_s*time/1000-4*Pi/3)*K*a;

elseif time<=810 then

f_s = f_N*a;

Rs = 0.531;

u_A = u_N * 1.414 * sin(2*Pi*f_s*time/1000)*a;

u_B = u_N * 1.414 * sin(2*Pi*f_s*time/1000-2*Pi/3)*a;

u_C = u_N * 1.414 * sin(2*Pi*f_s*time/1000-4*Pi/3)*a;

elseif time<=844 then

f_s = f_N*a;Rs = 2.5;

u_A = u_N * 1.414 * sin(2*Pi*f_s*time/1000-4*Pi/3)*a;

u_B = u_N * 1.414 * sin(2*Pi*f_s*time/1000-2*Pi/3)*a;

u_C = u_N * 1.414 * sin(2*Pi*f_s*time/1000)*a;

elseif time<=994 then

f_s = f_N*a;Rs = 0.531;

u_A = u_N * 1.414 * sin(2*Pi*f_s*time/1000-4*Pi/3)*a;

u_B = u_N * 1.414 * sin(2*Pi*f_s*time/1000-2*Pi/3)*a;

u_C = u_N * 1.414 * sin(2*Pi*f_s*time/1000)*a;

elseif time<=1495 then

u_A = u_N * 1.414 * sin(2*Pi*f_s*time/1000)*b;

u_B = u_N * 1.414 * sin(2*Pi*f_s*time/1000-2*Pi/3)*b;

u_C = u_N * 1.414 * sin(2*Pi*f_s*time/1000-4*Pi/3)*b;

f_s = f_N*b;Rs = 0.531;

elseif time<=1520 then

u_A = u_N * 1.414 * sin(2*Pi*f_s*time/1000-4*Pi/3)*K*c;

u_B = u_N * 1.414 * sin(2*Pi*f_s*time/1000-2*Pi/3)*K*c;

u_C = u_N * 1.414 * sin(2*Pi*f_s*time/1000)*K*c;

f_s = f_N*K*c;Rs = 0.531;

elseif time<=2250 then

u_A = u_N * 1.414 * sin(2*Pi*f_s*time/1000-4*Pi/3)*c;

u_B = u_N * 1.414 * sin(2*Pi*f_s*time/1000-2*Pi/3)*c;

u_C = u_N * 1.414 * sin(2*Pi*f_s*time/1000)*c;

f_s = f_N*c;Rs = 0.531;

elseif time<=2325 then

f_s = f_N*P*a;Rs = 2;

u_A = u_N * 1.414 * sin(2*Pi*f_s*time/1000)*a*P;

u_B = u_N * 1.414 * sin(2*Pi*f_s*time/1000-2*Pi/3)*a*P;

u_C = u_N * 1.414 * sin(2*Pi*f_s*time/1000-4*Pi/3)*a*P;

elseif time<=2465 then

f_s = f_N*a;Rs = 0.531;

u_A = u_N * 1.414 * sin(2*Pi*f_s*time/1000)*a;

u_B = u_N * 1.414 * sin(2*Pi*f_s*time/1000-2*Pi/3)*a;

u_C = u_N * 1.414 * sin(2*Pi*f_s*time/1000-4*Pi/3)*a;

 

else

u_A = u_N * 1.414 * sin(2*Pi*f_s*time/1000)*b;

u_B = u_N * 1.414 * sin(2*Pi*f_s*time/1000-2*Pi/3)*b;

u_C = u_N * 1.414 * sin(2*Pi*f_s*time/1000-4*Pi/3)*b;

f_s = f_N*b;Rs = 0.531;

end if;

 

end SACIM;

 

图像如下：

 

　　整个过程耗时2570ms，期间转矩Tm始终控制在200以下。